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-<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" |
- "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> |
- |
-<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> |
-<head> |
-<meta name="generator" content="HTML Tidy for Linux/x86 (vers 12 April 2005), see www.w3.org" /> |
-<title>Associative-Container Performance Tests</title> |
-<meta http-equiv="Content-Type" content="text/html; charset=us-ascii" /> |
-</head> |
-<body> |
-<div id="page"> |
-<h1><a name="assoc" id="assoc">Associative-Container |
- Performance Tests</a></h1> |
-<h2><a name="settings" id="settings">Settings</a></h2> |
-<p>This section describes performance tests and their results. |
- In the following, <a href="#gcc"><u>g++</u></a>, <a href="#msvc"><u>msvc++</u></a>, and <a href="#local"><u>local</u></a> (the build used for generating this |
- documentation) stand for three different builds:</p> |
-<div id="gcc_settings_div"> |
-<div class="c1"> |
-<h3><a name="gcc" id="gcc"><u>g++</u></a></h3> |
-<ul> |
-<li>CPU speed - cpu MHz : 2660.644</li> |
-<li>Memory - MemTotal: 484412 kB</li> |
-<li>Platform - |
- Linux-2.6.12-9-386-i686-with-debian-testing-unstable</li> |
-<li>Compiler - g++ (GCC) 4.0.2 20050808 (prerelease) |
- (Ubuntu 4.0.1-4ubuntu9) Copyright (C) 2005 Free Software |
- Foundation, Inc. This is free software; see the source |
- for copying conditions. There is NO warranty; not even |
- for MERCHANTABILITY or FITNESS FOR A PARTICULAR |
- PURPOSE.</li> |
-</ul> |
-</div> |
-<div class="c2"></div> |
-</div> |
-<div id="msvc_settings_div"> |
-<div class="c1"> |
-<h3><a name="msvc" id="msvc"><u>msvc++</u></a></h3> |
-<ul> |
-<li>CPU speed - cpu MHz : 2660.554</li> |
-<li>Memory - MemTotal: 484412 kB</li> |
-<li>Platform - Windows XP Pro</li> |
-<li>Compiler - Microsoft (R) 32-bit C/C++ Optimizing |
- Compiler Version 13.10.3077 for 80x86 Copyright (C) |
- Microsoft Corporation 1984-2002. All rights |
- reserved.</li> |
-</ul> |
-</div> |
-<div class="c2"></div> |
-</div> |
-<div id="local_settings_div"><div style = "border-style: dotted; border-width: 1px; border-color: lightgray"><h3><a name = "local"><u>local</u></a></h3><ul> |
-<li>CPU speed - cpu MHz : 2250.000</li> |
-<li>Memory - MemTotal: 2076248 kB</li> |
-<li>Platform - Linux-2.6.16-1.2133_FC5-i686-with-redhat-5-Bordeaux</li> |
-<li>Compiler - g++ (GCC) 4.1.1 20060525 (Red Hat 4.1.1-1) |
-Copyright (C) 2006 Free Software Foundation, Inc. |
-This is free software; see the source for copying conditions. There is NO |
-warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. |
-</li> |
-</ul> |
-</div><div style = "width: 100%; height: 20px"></div></div> |
-<h2><a name="assoc_tests" id="assoc_tests">Tests</a></h2> |
-<h3><a name="hash_based" id="hash_based">Hash-Based |
- Containers</a></h3> |
-<ol> |
-<li><a href="hash_text_find_find_timing_test.html">Hash-Based |
- Text <tt>find</tt> Find Timing Test</a></li> |
-<li><a href="hash_random_int_find_find_timing_test.html">Hash-Based |
- Random-Integer <tt>find</tt> Find Timing Test</a></li> |
-<li><a href="hash_random_int_subscript_find_timing_test.html">Hash-Based |
- Random-Integer Subscript Find Timing Test</a></li> |
-<li><a href="hash_random_int_subscript_insert_timing_test.html">Hash-Based |
- Random-Integer Subscript Insert Timing Test</a></li> |
-<li><a href="hash_zlob_random_int_find_find_timing_test.html">Hash-Based |
- Skewed-Distribution Random-Integer <tt>find</tt> Find Timing |
- Test</a></li> |
-<li><a href="hash_random_int_erase_mem_usage_test.html">Hash-Based Erase |
- Memory Use Test</a></li> |
-</ol> |
-<h3><a name="tree_like_based" id="tree_like_based">Tree-Like-Based Containers</a></h3> |
-<ol> |
-<li><a href="tree_text_insert_timing_test.html">Tree-Based |
- and Trie-Based Text Insert Timing Test</a></li> |
-<li><a href="tree_text_find_find_timing_test.html">Tree-Based |
- and Trie-Based Text <tt>find</tt> Find Timing Test</a></li> |
-<li><a href="tree_text_lor_find_find_timing_test.html">Tree-Based |
- Locality-of-Reference Text <tt>find</tt> Find Timing |
- Test</a></li> |
-<li><a href="tree_random_int_find_find_timing_test.html">Tree-Based |
- Random-Integer <tt>find</tt> Find Timing Test</a></li> |
-<li><a href="tree_split_join_timing_test.html">Tree Split and |
- Join Timing Test</a></li> |
-<li><a href="tree_order_statistics_timing_test.html">Tree |
- Order-Statistics Timing Test</a></li> |
-</ol> |
-<h3><a name="multimaps" id="multimaps">Multimaps</a></h3> |
-<ol> |
-<li><a href="multimap_text_find_timing_test_small.html">"Multimap" |
- Text Find Timing Test with <u>Small</u> Average Secondary-Key |
- to Primary-Key Ratio</a></li> |
-<li><a href="multimap_text_find_timing_test_large.html">"Multimap" |
- Text Find Timing Test with <u>Large</u> Average Secondary-Key |
- to Primary-Key Ratio</a></li> |
-<li><a href="multimap_text_insert_timing_test_small.html">"Multimap" |
- Text Insert Timing Test with <u>Small</u> Average |
- Secondary-Key to Primary-Key Ratio</a></li> |
-<li><a href="multimap_text_insert_timing_test_large.html">"Multimap" |
- Text Insert Timing Test with <u>Large</u> Average |
- Secondary-Key to Primary-Key Ratio</a></li> |
-<li><a href="multimap_text_insert_mem_usage_test_small.html">"Multimap" |
- Text Insert Memory-Use Test with <u>Small</u> Average |
- Secondary-Key to Primary-Key Ratio</a></li> |
-<li><a href="multimap_text_insert_mem_usage_test_large.html">"Multimap" |
- Text Insert Memory-Use Test with <u>Large</u> Average |
- Secondary-Key to Primary-Key Ratio</a></li> |
-</ol> |
-<h2><a name="assoc_observations" id="assoc_observations">Observations</a></h2> |
-<h3><a name="dss_family_choice" id="dss_family_choice">Underlying Data-Structure Families</a></h3> |
-<p>In general, hash-based containers (see <a href="hash_based_containers.html">Design::Associative |
- Containers::Hash-Based Containers</a>) have better timing |
- performance than containers based on different underlying-data |
- structures. The main reason to choose a tree-based (see |
- <a href="tree_based_containers.html">Design::Associative |
- Containers::Tree-Based Containers</a>) or trie-based container |
- (see <a href="trie_based_containers.html">Design::Associative |
- Containers::Trie-Based Containers</a>) is if a byproduct of the |
- tree-like structure is required: either order-preservation, or |
- the ability to utilize node invariants (see <a href="tree_based_containers.html#invariants">Design::Associative |
- Containers::Tree-Based Containers::Node Invariants</a> and |
- <a href="trie_based_containers.html#invariants">Design::Associative |
- Containers::Trie-Based Containers::Node Invariants</a>). If |
- memory-use is the major factor, an ordered-vector tree (see |
- <a href="tree_based_containers.html">Design::Associative |
- Containers::Tree-Based Containers</a>) gives optimal results |
- (albeit with high modificiation costs), and a list-based |
- container (see <a href="lu_based_containers.html">Design::Associative |
- Containers::List-Based Containers</a>) gives reasonable |
- results.</p> |
-<h3><a name="hash_based_types" id="hash_based_types">Hash-Based |
- Container Types</a></h3> |
-<p>Hash-based containers are typically either collision |
- chaining or probing (see <a href="hash_based_containers.html">Design::Associative |
- Containers::Hash-Based Containers</a>). Collision-chaining |
- containers are more flexible internally, and so offer better |
- timing performance. Probing containers, if used for simple |
- value-types, manage memory more efficiently (they perform far |
- fewer allocation-related calls). In general, therefore, a |
- collision-chaining table should be used. A probing container, |
- conversely, might be used efficiently for operations such as |
- eliminating duplicates in a sequence, or counting the number of |
- occurrences within a sequence. Probing containers might be more |
- useful also in multithreaded applications where each thread |
- manipulates a hash-based container: in the STL, allocators have |
- class-wise semantics (see [<a href="references.html#meyers96more">meyers96more</a>] - Item 10); a |
- probing container might incur less contention in this case.</p> |
-<h3><a name="hash_based_policies" id="hash_based_policies">Hash-Based Containers' Policies</a></h3> |
-<p>In hash-based containers, the range-hashing scheme (see |
- <a href="hash_based_containers.html#hash_policies">Design::Associative |
- Containers::Hash-Based Containers::Hash Policies</a>) seems to |
- affect performance more than other considerations. In most |
- settings, a mask-based scheme works well (or can be made to |
- work well). If the key-distribution can be estimated a-priori, |
- a simple hash function can produce nearly uniform hash-value |
- distribution. In many other cases (<i>e.g.</i>, text hashing, |
- floating-point hashing), the hash function is powerful enough |
- to generate hash values with good uniformity properties |
- [<a href="references.html#knuth98sorting">knuth98sorting</a>]; |
- a modulo-based scheme, taking into account all bits of the hash |
- value, appears to overlap the hash function in its effort.</p> |
-<p>The range-hashing scheme determines many of the other |
- policies (see <a href="hash_based_containers.html#policy_interaction">Design::Hash-Based |
- Containers::Policy Interaction</a>). A mask-based scheme works |
- well with an exponential-size policy (see <a href="hash_based_containers.html#resize_policies">Design::Associative |
- Containers::Hash-Based Containers::Resize Policies</a>) ; for |
- probing-based containers, it goes well with a linear-probe |
- function (see <a href="hash_based_containers.html#hash_policies">Design::Associative |
- Containers::Hash-Based Containers::Hash Policies</a>).</p> |
-<p>An orthogonal consideration is the trigger policy (see |
- <a href="hash_based_containers.html#resize_policies">Design::Associative |
- Containers::Hash-Based Containers::Resize Policies</a>). This |
- presents difficult tradeoffs. <i>E.g.</i>, different load |
- factors in a load-check trigger policy yield a |
- space/amortized-cost tradeoff.</p> |
-<h3><a name="tree_like_based_types" id="tree_like_based_types">Tree-Like-Based Container |
- Types</a></h3> |
-<p>In general, there are several families of tree-based |
- underlying data structures: balanced node-based trees |
- (<i>e.g.</i>, red-black or AVL trees), high-probability |
- balanced node-based trees (<i>e.g.</i>, random treaps or |
- skip-lists), competitive node-based trees (<i>e.g.</i>, splay |
- trees), vector-based "trees", and tries. (Additionally, there |
- are disk-residing or network-residing trees, such as B-Trees |
- and their numerous variants. An interface for this would have |
- to deal with the execution model and ACID guarantees; this is |
- out of the scope of this library.) Following are some |
- observations on their application to different settings.</p> |
-<p>Of the balanced node-based trees, this library includes a |
- red-black tree (see <a href="tree_based_containers.html">Design::Associative |
- Containers::Tree-Based Containers</a>), as does STL (in |
- practice). This type of tree is the "workhorse" of tree-based |
- containers: it offers both reasonable modification and |
- reasonable lookup time. Unfortunately, this data structure |
- stores a huge amount of metadata. Each node must contain, |
- besides a value, three pointers and a boolean. This type might |
- be avoided if space is at a premium [<a href="references.html#austern00noset">austern00noset</a>].</p> |
-<p>High-probability balanced node-based trees suffer the |
- drawbacks of deterministic balanced trees. Although they are |
- fascinating data structures, preliminary tests with them showed |
- their performance was worse than red-black trees. The library |
- does not contain any such trees, therefore.</p> |
-<p>Competitive node-based trees have two drawbacks. They are |
- usually somewhat unbalanced, and they perform a large number of |
- comparisons. Balanced trees perform one comparison per each |
- node they encounter on a search path; a splay tree performs two |
- comparisons. If the keys are complex objects, <i>e.g.</i>, |
- <tt>std::string</tt>, this can increase the running time. |
- Conversely, such trees do well when there is much locality of |
- reference. It is difficult to determine in which case to prefer |
- such trees over balanced trees. This library includes a splay |
- tree (see <a href="tree_based_containers.html">Design::Associative |
- Containers::Tree-Based Containers</a>).</p> |
-<p>Ordered-vector trees (see <a href="tree_based_containers.html">Design::Associative |
- Containers::Tree-Based Containers</a>) use very little space |
- [<a href="references.html#austern00noset">austern00noset</a>]. |
- They do not have any other advantages (at least in this |
- implementation).</p> |
-<p>Large-fan-out PATRICIA tries (see <a href="trie_based_containers.html">Design::Associative |
- Containers::Trie-Based Containers</a>) have excellent lookup |
- performance, but they do so through maintaining, for each node, |
- a miniature "hash-table". Their space efficiency is low, and |
- their modification performance is bad. These tries might be |
- used for semi-static settings, where order preservation is |
- important. Alternatively, red-black trees cross-referenced with |
- hash tables can be used. [<a href="references.html#okasaki98mereable">okasaki98mereable</a>] |
- discusses small-fan-out PATRICIA tries for integers, but the |
- cited results seem to indicate that the amortized cost of |
- maintaining such trees is higher than that of balanced trees. |
- Moderate-fan-out trees might be useful for sequences where each |
- element has a limited number of choices, <i>e.g.</i>, DNA |
- strings (see <a href="assoc_examples.html#trie_based">Examples::Associative |
- Containers::Trie-Based Containers</a>).</p> |
-<h3><a name="msc" id="msc">Mapping-Semantics |
- Considerations</a></h3> |
-<p>Different mapping semantics were discussed in <a href="motivation.html#assoc_mapping_semantics">Motivation::Associative |
- Containers::Alternative to Multiple Equivalent Keys</a> and |
- <a href="tutorial.html#assoc_ms">Tutorial::Associative |
- Containers::Associative Containers Others than Maps</a>. We |
- will focus here on the case where a keys can be composed into |
- primary keys and secondary keys. (In the case where some keys |
- are completely identical, it is trivial that one should use an |
- associative container mapping values to size types.) In this |
- case there are (at least) five possibilities:</p> |
-<ol> |
-<li>Use an associative container that allows equivalent-key |
- values (such as <tt>std::multimap</tt>)</li> |
-<li>Use a unique-key value associative container that maps |
- each primary key to some complex associative container of |
- secondary keys, say a tree-based or hash-based container (see |
- <a href="tree_based_containers.html">Design::Associative |
- Containers::Tree-Based Containers</a> and <a href="hash_based_containers.html">Design::Associative |
- Containers::Hash-Based Containers</a>)</li> |
-<li>Use a unique-key value associative container that maps |
- each primary key to some simple associative container of |
- secondary keys, say a list-based container (see <a href="lu_based_containers.html">Design::Associative |
- Containers::List-Based Containers</a>)</li> |
-<li>Use a unique-key value associative container that maps |
- each primary key to some non-associative container |
- (<i>e.g.</i>, <tt>std::vector</tt>)</li> |
-<li>Use a unique-key value associative container that takes |
- into account both primary and secondary keys.</li> |
-</ol> |
-<p>We do not think there is a simple answer for this (excluding |
- option 1, which we think should be avoided in all cases).</p> |
-<p>If the expected ratio of secondary keys to primary keys is |
- small, then 3 and 4 seem reasonable. Both types of secondary |
- containers are relatively lightweight (in terms of memory use |
- and construction time), and so creating an entire container |
- object for each primary key is not too expensive. Option 4 |
- might be preferable to option 3 if changing the secondary key |
- of some primary key is frequent - one cannot modify an |
- associative container's key, and the only possibility, |
- therefore, is erasing the secondary key and inserting another |
- one instead; a non-associative container, conversely, can |
- support in-place modification. The actual cost of erasing a |
- secondary key and inserting another one depends also on the |
- allocator used for secondary associative-containers (The tests |
- above used the standard allocator, but in practice one might |
- choose to use, <i>e.g.</i>, [<a href="references.html#boost_pool">boost_pool</a>]). Option 2 is |
- definitely an overkill in this case. Option 1 loses out either |
- immediately (when there is one secondary key per primary key) |
- or almost immediately after that. Option 5 has the same |
- drawbacks as option 2, but it has the additional drawback that |
- finding all values whose primary key is equivalent to some key, |
- might be linear in the total number of values stored (for |
- example, if using a hash-based container).</p> |
-<p>If the expected ratio of secondary keys to primary keys is |
- large, then the answer is more complicated. It depends on the |
- distribution of secondary keys to primary keys, the |
- distribution of accesses according to primary keys, and the |
- types of operations most frequent.</p> |
-<p>To be more precise, assume there are <i>m</i> primary keys, |
- primary key <i>i</i> is mapped to <i>n<sub>i</sub></i> |
- secondary keys, and each primary key is mapped, on average, to |
- <i>n</i> secondary keys (<i>i.e.</i>, |
- <i><b>E</b>(n<sub>i</sub>) = n</i>).</p> |
-<p>Suppose one wants to find a specific pair of primary and |
- secondary keys. Using 1 with a tree based container |
- (<tt>std::multimap</tt>), the expected cost is |
- <i><b>E</b>(Θ(log(m) + n<sub>i</sub>)) = Θ(log(m) + |
- n)</i>; using 1 with a hash-based container |
- (<tt>std::tr1::unordered_multimap</tt>), the expected cost is |
- <i>Θ(n)</i>. Using 2 with a primary hash-based container |
- and secondary hash-based containers, the expected cost is |
- <i>O(1)</i>; using 2 with a primary tree-based container and |
- secondary tree-based containers, the expected cost is (using |
- the Jensen inequality [<a href="references.html#motwani95random">motwani95random</a>]) |
- <i><b>E</b>(O(log(m) + log(n<sub>i</sub>)) = O(log(m)) + |
- <b>E</b>(O(log(n<sub>i</sub>)) = O(log(m)) + O(log(n))</i>, |
- assuming that primary keys are accessed equiprobably. 3 and 4 |
- are similar to 1, but with lower constants. Using 5 with a |
- hash-based container, the expected cost is <i>O(1)</i>; using 5 |
- with a tree based container, the cost is |
- <i><b>E</b>(Θ(log(mn))) = Θ(log(m) + |
- log(n))</i>.</p> |
-<p>Suppose one needs the values whose primary key matches some |
- given key. Using 1 with a hash-based container, the expected |
- cost is <i>Θ(n)</i>, but the values will not be ordered |
- by secondary keys (which may or may not be required); using 1 |
- with a tree-based container, the expected cost is |
- <i>Θ(log(m) + n)</i>, but with high constants; again the |
- values will not be ordered by secondary keys. 2, 3, and 4 are |
- similar to 1, but typically with lower constants (and, |
- additionally, if one uses a tree-based container for secondary |
- keys, they will be ordered). Using 5 with a hash-based |
- container, the cost is <i>Θ(mn)</i>.</p> |
-<p>Suppose one wants to assign to a primary key all secondary |
- keys assigned to a different primary key. Using 1 with a |
- hash-based container, the expected cost is <i>Θ(n)</i>, |
- but with very high constants; using 1 with a tree-based |
- container, the cost is <i>Θ(nlog(mn))</i>. Using 2, 3, |
- and 4, the expected cost is <i>Θ(n)</i>, but typically |
- with far lower costs than 1. 5 is similar to 1.</p> |
-</div> |
-</body> |
-</html> |